“ To unfold the secret laws and relations of those high faculties of thought by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind.” -George Boole
You can attribute the logical foundation of computing to the famous mathematician and philosopher George Boole. His seminal work, commonly referred to as The Laws of Thought, investigates the foundational laws of the mind through logical operations.
The idea was simple, we can reduce the arguments and structure of ordinary language down to the syntactical form of which we may derive a symbolic logic. Take the sentence; If it is hot outside I am going to wear shorts. We can reduce this to If P (hot outside) then Q (going to wear shorts). We can see that we can completely set aside the meaning of that sentence and make it syntactical. In this way we can preserve truth. If our proposition is true, then we know our conclusion will be as well. I know that since, for example, it is hot I am going to wear shorts.
Computers are exactly the device that can preserve truth. It can implement logic and handle all the syntax. This is awesome because we can now put thought into machines, all we have to do is give these logical sentences meaning! Thought is logic, we have computers which can do logic therefore machines can think!
The first truth preservation device, a logical machine, was made by Alan Turing. He also had come up with this Theoretical Device, known today as the Turing Machine, with which gives us a way to think about what our minds are doing.
A Turing machine is a conceptual (and possible) machine which takes and encodes a table of inputs and turns them into logical symbols as outputs, then those outputs are then taken into another Turing machine, and the same process continues, over and over, until we have this Universal Machine that replicates the behaviour of any Turing Machine. This single Universal Machine, is essentially an algorithmic process. Anything that can be computed a Turing Machine can do.
So what does all this stuff about the foundations of logic, Turing Machines and algorithms have to do with Artificial Intelligence???
Well Turing proves that having a general artificial intelligent system is possible! If we think about the mind as doing computations, the algorithmic process of changing the meaning into symbols, then we simply just need a large enough computer that does everything the mind can do. A computer could simulate a mind!
Good Old Fashioned Artificial Intelligence
You might be wondering if any of this logical thinking mind computer stuff I am talking about has any basis in reality. Has this actually been put to the test? Can we really simulate an intelligent system through simply logical terms?
Two researcher back in the 50s, Allen Newell and Herbert Simon, from Dartmouth thought they had come up with the thinking machine. There Logic Theory machine had been able to create more elegant mathematical proofs formed from logical axioms of Bertrand Russel’s Principia Mathematica.
This was all well and good, but it faced a major problem. Humans as a thinking machine have to deal with a dynamic environment in which we have a potentially indefinite set of possible decisions that we can make. They needed a process, a heuristic, in which can simplify the problem space to find adequate solutions instead of the best ones. To think like a human might.
Newell and Simon set out to create a General Problem Solver. To employ heuristic under the new research from the success and failures of the Logical Thinking Machine.
Newell and Simon were able to find some success from there implementations using logical puzzles like the classic cannibals and missionaries problem.
Newell and Simon found out that thinking or problem solving, the information processing in human intelligence, is not simply on how we are able to symbolically formalize and compute logical statements, but also on how we even formulate the problem in the first place. Given all the computational complexity that we could encounter, we cannot simply be a Logical Machine, have biological limitations living in dynamic situations.
There must be more to human intelligence then simply logical processing.
In conclusion, Artificial intelligence shares a deep and insightful history with modern logic. From Boole’s simple probability theories and its theoretical foundations in thinking, to Turing Machines proving the possibility of logical thinking to Newell and Simon attempts at a General Problem Solver. The history of A.I is already rich. The work done by these outstanding intellectuals has shaped the considerations we make on problems with language, vision and general intelligence. Thus, the foundations of modern logic, and the use of logic in A.I is intimately linked allowing us to come much closer to mechanizing our minds!